three-doors-game-show.m

% Program:
% three-doors-game-show.m
% Three doors game show stastical simulation.
% 
% Simulates a game show where the contestant attempts to pick the correct 
% one of three doors. The program shows the statistical odds of winning 
% based on two strategies. The first strategy is to not switch doors when
% given the opportunity. The second strategy is to always switch doors when
% given the opportunity.
%
% Variable List:
% Always_Switch_Doors = Strategy switch
% Iterations = Number of times to simulate
% Run = Current run number
% Door_Setup = Number to determine door setup
% Door = Current door setup
% Door_Chosen = Door chosen by contestant
% Door_Removed = Door removed by host
% Wins = Total number of wins
% Losses = Total number of losses
% Percent = Percentage of games won
% n = Counter

clear, clc                              % Clear command window and workspace

Always_Switch_Doors = 1;                % Always switch doors?
Iterations = 1000;                      % Number of iterations
Wins = 0;                               % Initialize wins

for Run = 1:Iterations                  % Iterations to run
    fprintf('Run = %i \n', Run);
    Door_Setup = randi([1,3]);          % Generate random door scenario
    switch Door_Setup
        case 1                          % Scenario 1
            Door = {'Car';
                    'Goat';
                    'Goat'};
        case 2                          % Scenario 2
            Door = {'Goat'; 
                    'Car';
                    'Goat'};
        case 3                          % Scenario 3
            Door = {'Goat';
                    'Goat'; 
                    'Car'};
    end
    fprintf('Doors = %s %s %s \n', Door{1}, Door{2}, Door{3});

    Door_Chosen = randi([1,3]);             % Generate random door number
    fprintf('Door_Chosen = %i \n', Door_Chosen);

    while 1;
        Door_Removed = randi([1,3]);        % Choose random door to remove
        if strcmp(Door(Door_Removed), 'Goat') && Door_Removed ~= Door_Chosen;
            break                           % Remove a door with a goat
        end
    end
    fprintf('Door_Removed = %i \n', Door_Removed);

    switch Always_Switch_Doors              % Switch doors if switch is on
       case 0                               % Do not switch doors         
          fprintf('Not Switching Doors \n');
          fprintf('Door_Chosen = %i \n', Door_Chosen);
       case 1                               % Switch doors
           for n = 1:3
               if n ~= Door_Chosen && n ~= Door_Removed;
                   Door_Chosen = n;         % Final door selected
                   fprintf('Switching Doors \n');
                   fprintf('Door_Chosen = %i \n', Door_Chosen);
                   break
               end
           end
    end
    
    if strcmp(Door(Door_Chosen), 'Car');    % Winner if car door is chosen
        fprintf('Win \n \n');
        Wins = Wins + 1;                    % Increment win counter
    else
        fprintf('Lose \n \n');
    end   
end
 
Losses = Iterations - Wins;                 % Record simulation statistics
Percent = Wins/Iterations*100;              % Percentage of games won
fprintf(['Always Switch = %1.1i, Wins = %1.1i, Losses = %1.1i,' ...
    'Percentage = %1.1f \n'], Always_Switch_Doors, Wins, Losses, Percent);